Others have mentioned other reasons, but here's another that I find particularly compelling.

In a game of D&D, it is generally accepted that the DM will build combat encounters to be difficult for the characters no matter what level they are at. This can lead to a pattern where your players feel as though, even with all the new powers they are getting, they are still weak.

Giving them a combat or two that is low level can remind the players how far they've come, especially if you choose similar enemies to a well-remembered early combat. For example, if your campaign opened on a difficult battle against a group of wolves, tossing some wolves at your now 8th-level players can help them feel as though they have grown in power.

It's a way to reward players for making progression and leveling up. It shows them that, even though on the game's main course they will always be challenged, they are still very powerful individuals, apart from the rest of the world.

It's a way to help them personally experience how far they've come, instead of just telling them so using numbers on their sheet.

Combat as a mechanical resource

If you are using XP progression (which is the default way to play, according to the PHB) and you want to give your player characters some catching-up, then you could use an easy combat encounter for this purpose. Similarly, you could give the party items as a reward from such encounters.

Combat as a pacing tool

While D&D is essentially a combat engine, not all campaigns are heavy on combat. Often, story-driven or intrigue campaigns tend to be light on combat. They may essentially involve the party going from location A to location B. If the players seem to get bored by this pace, the DM could add the occasional easy combat encounter to maintain player engagement.

For example, if the party is traveling by ship and the DM wants the voyage to seem more substantial than a scene transition, then an encounter with mutineering pirates or ambushing sahuagins could make the voyage more interesting.

Combat as storytelling

When you narrate your game world, the DM's medium isn't limited to the words they say when the player characters walk into the dungeon and look around. Instead of communicating via exposition, the DM can use interactive in-game challenges to convey the same message.

Much like how environmental exploration can be a means of storytelling, you can use combat encounters as a form of narration, worldbuilding, and foreshadowing. For example, the DM may communicate that a crypt is infested with undead via hostile undead, rather than exposition. Or, suppose the PCs are exploring a forest with a big bad CR 3 Winter Wolf at the end, and the DM wants to foreshadow "Here be wolves." Instead of exposition via NPC dialogue or narration, they could instead send some CR 1/4 Wolves as a greeting party.

Disclaimer: Adding extra combats is not universally beneficial to every game, especially when time is limited. Eschewing combat in favor of a battle summary ("You stab the goblin and get 100 XP and 5 gp") or narration ("The sign says there are zombies inside") is more efficient than a time-consuming battle, but potentially less engaging. However, for the reasons given above, these extra easy combats can be beneficial to some games, and the DM should consider the tradeoffs before adding them to their campaign.

Because it's fun

The purpose of the game isn't to accumulate, track and expend resources, it's to enjoy the process. Combat encounters are a major part of the major (though not all!) RPG game system designs because many people like to play combat encounters. For example, one can think of D&D 4E as a foray towards 'tactical combat boardgame', which is an attraction for some groups and a detraction for others.

Challenges are not resource costs

There does need to be some feeling of a challenge and risk involved to improve involvement, but that's IMHO orthogonal to resource expenditure - there's no meaningful difference between "Oh, we're just going to smash these goblins so it doesn't matter how we proceed, let's just skip rolling the dice and write down the xp and loot" and "Oh, we're just going to smash these goblins so it doesn't matter how we proceed, let's just skip rolling the dice and write down the xp and loot, and cross out some ammo, wand charges and a healing potion".

In both cases we play out the combat encounter (instead of reducing it to the abovementioned sentences) if and only if it's fun to do, not because we want to accurately track expended resources. Groups who don't enjoy playing out encounters without a story impact shouldn't play them out in detail even if it'd be a hard encounter that costs resources. If your story, setting and group fits that, then it'd be appropriate to just say "while you're resting for the night, a bunch of wolves attack your camp. You defeat them, but it costs you resources X, Y and Z". And if your group enjoys playing out tactical combat, then they'll likely want to play out also scenarios where they have an advantage.

There are various games which do explicitly handle challenges as resource costs i.e. "spend X, or get consequences Y". In most of its forms, D&D isn't really one of these systems. It can be used like this, depending on the DM, but it intentionally has a lot of "heavyweight" combat mechanics designed to play out encounters in tactical detail, instead of resolving them as a resource metagame. After all, D&D early origins come from the miniature wargaming community, and it's reflected even in 5e rules.

Variety breathes life in the game.

D&D is not a video game where the difficulty of an encounter is carefully tailored to always be Medium/Hard for the current group of players.

Instead, I have found that a variety of difficulties makes encounters more fun.

Just like various foes should react differently, various foes should present different difficulty levels. For example it is unrealistic that the cities gatekeepers, paid a couple coppers a day, be a real challenge to a high-level party... but it may not prevent said gatekeepers from challenging the party nonetheless.

Varying difficulty levels make the World take a life on its own, rather than strictly revolving around the party. It gives a more "sandbox" feel.

Variety fosters Role-Play.

Similarly, variety limits meta-gaming and fosters role-play.

If the players are used to always encountering a certain level of difficulty, they will adapt their gameplay: they know that an encounter requires a certain amount of buffing, and the expenditure of a certain amount of resources (spells, potions, etc...), so as combat starts the Cleric casts a protective spell... "as usual".

Instead, when the difficulty of encounters swings wildly between Easy and Deadly (or Impossible), and cannot be "meta-gamed", then the players have to proceed cautiously, and have to use their characters' knowledge and interactions to suss out how strong the opposition really is.

Personally I find it more realistic.

I would note that this does not mean that the combat should become boring and sluggish. The DM is in position to shorten the fight by having the opposition flee or throw down their weapons when they realize how hopeless the fight is... such as after just witnessed one of their allies getting cleaved in two in a single swing by the Big Bad Fighter.

There are two reasons I use those now and again

1. 
   

   Sometimes, the players need to feel successful.

   
   
   

   I use this particularly with new players, and with younger players when I deem that a tougher encounter might go badly.

   
   


2. 
   

   Sometimes, the party's foes make a mistake.

   
   
   

   Just as the PCs can now and again underestimate how hard an encounter or monster is, the reverse is true. This is more of a narrative based approach, and works either in an ambush scenario (where the bandits really don't know who they are messing with) or after a social situation when the reaction by the party's opponent leads to blows (due to ego, anger, surprise reveal of pet peeve, or something else on the part of the opponent/leader). In a case like this, social to combat transition, if there are a goodly sized number of opponents, some of them fleeing or surrendering if the party begins to beat the stuffing out of them is a common result. That leads to a non combat encounter/situation: what do we do with these prisoners?

   
   


3. 
   

   A last reason that I no longer use with our current group: to get
   the party used to not expending resources as a reflex.

   
   
   

   A group of old timers had developed the habit of going nova early since I tended to run 3 or 4 encounters at the hard - deadly level. (I tend to backwards budget daily XP budget to make encounter bundles). On the fourth encounter of that day, I went 'easy to medium' since they had no spell slots left, but there were still plenty of enemies in the area. The party won handily except that one character had to make a death save due to getting hit by a crit. The crit / damage spike phenomenon is part of the swinginess of the d20 system. (I don't do this anymore since there is a limit to how many new tricks old dogs will learn.)

   
   

@Matthieu'sM's point on variety making for a fun game experience is something I've seen at tables from both sides of the screen.

I have used easy encounters several times in my campaign, for two reasons:

1. They've made a right decision or succeeded a roll, usually sneak or deception to lure some enemies away.


2. I have a player that likes combat.

An example is when they were tracking bandits to their hideout. They succeeded perception roll to find a hidden passage right into the abandoned castle, where there were only 1-2 guards, as opposed to 4-5 guards on the main gate.

The easy encounter is given to give a sense of accomplishment for choosing the right option or succeeding an important roll (and make sure later they know what would happened if they choose the wrong option or failed the roll).

I also still put the encounter there, although I can easily narrate they beat the guards easily, to give at least one encounter per session for this player. He is happy with this arrangement, and the others too (usually the encounter only lasted 10 minutes).

To reduce player paranoia

If players expect each combat encounter to be deadly or at least to consume a significant amount of resources they will approach the game very carefully. That means more of the game time is spent on planning instead of action.
In extreme cases it can lead to players anticipating to encounter danger even when there isn't any or trying to avoid combat at any cost. This is similar to how springing deadly traps upon players will make them check every nook and cranny before proceeding and can significantly slow down the game.

By occasionally introducing an encounter that can be won without any planning, complicated tactics or significant losses you can encourage players to be bolder and take more risks in the future. It could also speed up gameplay and even make player actions more varied if they don't feel pressured to make the most optimal choice every turn.

While watching players overcome the odds against a difficult encounter is undoubtedly fun, sometimes it is more fun to watch them charge recklessly into the fray, which they won't do if they know it will end up badly.

Some people like it.

Take a look at page 6 of your DMG. (It's a fantastic resource.) One of the player types there just wants to be awesome in combat. They may or may not enjoy tactical challenge. They do enjoy the idea of charging into a horde of orcs, and hitting one orc so hard that his head comes flying off and strikes another orc, killing both of them on the spot. This is the part of the game that that player really gets into. Now, if you're a player who's really into tactical optimization and balancing resources and so forth, there isn't going to be a lot of appeal, but if you're that kind of player, then Easy encounters aren't really for you. They're for the kind of player that likes to be reminded from time to time that, as a sixth-level barbarian, they really are a raging badass that most people would have reason to be rightly terrified of.

It's a refreshing break

Shakespeare had humorous scenes even in the middle of his tragedies. You can, too. Giving the players an opportunity to cut loose on some hapless foes who aren't a meaningful threat and maybe show off a bit can offer a mental break in the middle of an otherwise grindingly difficult dungeon. That both gives them a bit of mental recovery time and means that when they jump back into the trenches, it hits them fresh again. Both effects can be worthwhile for crafting the experience.